{"id":4815,"date":"2023-03-09T10:43:44","date_gmt":"2023-03-09T15:43:44","guid":{"rendered":"http:\/\/matroidunion.org\/?p=4815"},"modified":"2023-03-22T19:48:24","modified_gmt":"2023-03-22T23:48:24","slug":"online-talk-matthew-kroeker","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=4815","title":{"rendered":"Online Talk: Matthew Kroeker"},"content":{"rendered":"\n<p><strong>YouTube recording:<\/strong> <a href=\"https:\/\/www.youtube.com\/watch?v=2ga1XlPid9c\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=2ga1XlPid9c<\/a><\/p>\n<p><strong>Time: <\/strong>Thursday, Mar 16, 3pm ET (beware of U.S.\/Canada time change on Mar 12!)<br \/><strong>Zoom: <\/strong><a href=\"https:\/\/uwaterloo.zoom.us\/j\/94977150195?pwd=LzRHN3NVcWtGbWlOVGNmakJQenF1Zz09\" target=\"_blank\" rel=\"noopener\">https:\/\/uwaterloo.zoom.us\/j\/94977150195<br \/>pwd=LzRHN3NVcWtGbWlOVGNmakJQenF1Zz09<\/a><br \/><strong>Passcode:<\/strong> kroeker1<br \/><br \/><strong>Speaker:<\/strong> Matthew Kroeker, University of Waterloo<br \/><strong>Title: <\/strong>Unavoidable Flats in Matroids Representable over a Prime Field<br \/><br \/><strong>Abstract: <\/strong>The Sylvester-Gallai Theorem says that every rank-3 real-representable matroid contains a two-point line. A high-dimensional generalization of this result, due to Hansen, implies that every simple real-representable matroid of sufficiently high rank contains a rank-k independent flat. One only needs to look as far as the binary projective plane to see that such a result cannot hold for the class of matroids representable over a finite field. In light of this, we ask whether it is possible to determine a small list of \u201cunavoidable\u201d rank-k flats guaranteed to exist in a simple GF(q)-representable matroid of sufficiently high rank. We will answer this question for the case of prime fields: in particular, we show that, for any prime p and positive integer k, any simple GF(p)-representable matroid of sufficiently high rank contains a rank-k flat which is either independent, or is a projective or affine geometry. This is joint work with Jim Geelen.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YouTube recording: https:\/\/www.youtube.com\/watch?v=2ga1XlPid9c Time: Thursday, Mar 16, 3pm ET (beware of U.S.\/Canada time change on Mar 12!)Zoom: https:\/\/uwaterloo.zoom.us\/j\/94977150195pwd=LzRHN3NVcWtGbWlOVGNmakJQenF1Zz09Passcode: kroeker1 Speaker: Matthew Kroeker, University of WaterlooTitle: Unavoidable Flats in Matroids Representable over a Prime Field Abstract: The Sylvester-Gallai Theorem says that &hellip; <a href=\"https:\/\/matroidunion.org\/?p=4815\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":21,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11],"class_list":["post-4815","post","type-post","status-publish","format-standard","hentry","category-matroids","tag-online-talks"],"_links":{"self":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4815","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/users\/21"}],"replies":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4815"}],"version-history":[{"count":3,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4815\/revisions"}],"predecessor-version":[{"id":4828,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4815\/revisions\/4828"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4815"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4815"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4815"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}